A356334 - OEIS

%I #33 Sep 21 2022 21:24:44

%S 1,3,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3

%N a(n) is the number of nonnegative integer solutions (x; y) with x <= y of x^(n+1) + y^(n+1) = (x+y)^n.

%C Conjecture: a(n) = 3 except for n = 0 or n = 2. - _Chai Wah Wu_, Sep 21 2022

%e For n=2, the 4 solutions are (0; 0), (0; 1), (1; 2) and (2; 2). The pairs (0; 0), (0; 1) and (2^(n-1); 2^(n-1)) exist for all n > 0.

%o (Python)

%o def A356334(n): return sum(1 for x in range((1<<n)+1) for y in range(x,(1<<n)+1) if x**(n+1)+y**(n+1)==(x+y)**n) # _Chai Wah Wu_, Sep 19 2022

%K nonn,more

%O 0,2

%A _Reiner Moewald_, Aug 04 2022

%E a(11)-a(14) from _Hugo Pfoertner_, Sep 18 2022

%E a(15)-a(20) from _Chai Wah Wu_, Sep 21 2022